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pQCD A.) pQCD components in elementary collisions B.) modification in AA collisions
High pT Particle Production (the factorization theorem) Jet: A localized collection of hadrons which come from a fragmenting parton
hadrons
c
a
Parton Distribution Functions Hard-scattering cross-section
b
d hadrons
Fragmentation Function
leading particle
High pT (> ~ 2.0 GeV/c) hadron production in pp collisions for √s > 60 Gev: h d pp
0 D d 2 2 h/c K dx dx f ( x , Q ) f ( x , Q ) ( ab cd ) a b a a b b 2 dyd pT dtˆ z c abcd
“Collinear factorization”
Hard scattering longitudinal plane Hard scattering in transverse plane
Generally, partons momentum fraction x1x2. Point-like elastic scattering
Partons have intrinsic transverse momentum kT
(Not pT , jetin1 PHENIX pT , jet –0.350 + X
Thermallyshaped Soft Production
“Well Calibrated” Hard Scattering
Ingredients (via KKP or Kretzer) pQCD Parton distribution functions Fragmentation functions ..or simply PYTHIA… hep-ex/0305013 S.S. Adler et al.
pp at RHIC: Strangeness formation in QCD nucl-ex/0607033
Strangeness production not described by leading order calculation (contrary to pion production). It needs multiple parton scattering (e.g. EPOS) or NLO corrections to describe strangeness production. Part of it is a mass effect (plus a baryon-meson effect) but in addition there is a strangeness ‘penalty’ factor (e.g. the proton fragmentation function does not describe L production). s is not just another light quark
How strong are the NLO corrections in LO calculations (PYTHIA) ?
K.Eskola et al. (NPA 713 (2003)): Large NLO corrections not unreasonable at RHIC energies.
Should be negligible at LHC (5.5 or 14 TeV).
STAR
LHC
New NLO calculation based on STAR data (AKK, hep-ph/0502188, Nucl.Phys.B734 (2006))
K0s
apparent Einc dependence of separated quark contributions.
Non-strange baryon spectra in p+p
Pions agree with LO (PYTHIA) Protons require NLO with AKK-FF parametrization (quark separated FF contributions)
PLB 637 (2006) 161
mt scaling in pp
Breakdown of mT scaling in pp ?
mT slopes from PYTHIA 6.3
Gluon dominance at RHIC PYTHIA: Di-quark structures in baryon production cause mt-shift Recombination: 2 vs 3 quark structure causes mt shift
Baryon/meson ratios – p+p collisions
PLB 637 (2006) 161
Bell shape from fragmentation is visible
Collision Energy dependence of baryon/meson ratio Ratio vs pT seems very energy dependent (RHIC < < SPS or FNAL), LHC ? Not described by fragmentation ! (PYTHIA ratios at RHIC and FNAL are equal) Additional increase with system size in AA
Both effects (energy and system size dependence) well described by recombination
Recombination vs. Fragmentation (a different hadronization mechanism in medium than in vacuum ?) Recombination at moderate PT
Parton pt shifts to higher hadron pt. Recomb. Fragmentation at high PT:
Parton pt shifts to lower hadron pT
fragmenting parton: ph = z p, z> mc where mass is not relevant Calculations depend on quark mass mc, factorization scale F (typically F = mc or 2 mc), renormalization scale R (typically R = F), parton density functions (PDF) Hard to obtain large with R = F (which is used in PDF fits)
FONLL RHIC (from hep-ph/0502203 ):
400 NLO 381 cFONLL 256 b ; 244 c 146 cc 134 b 99 bbFONLL 1.8700..67 b
NLO:
CDF Run II c to D data (PRL 91,241804 (2003): The non-perturbative charm fragmentation needed to be tweaked in FONLL to describe charm. FFFONLL is much harder than used before in ‘plain’ NLO FFFONLL ≠ FFNLO
RHIC: FONLL versus Data cc (STAR from D 0 eTOF ) cc ( FONLL)
Matteo Cacciari (FONLL): factor 2 is not a problem hep-ex/0609010 factor 5 is !!!
nucl-ex/0607012
Spectra in pp seem to require a bottom contribution High precision heavy quark measurements are tough at RHIC energies. Need direct reconstruction instead of semi-leptonic decays. Easy at LHC.
Conclusions for RHIC pp data
We are mapping out fragmentation and hadronization in vacuum as a function of flavor. What we have learned:
Strong NLO contribution to fragmentation even for light quarks at RHIC energies Quark separation in fragmentation function very important. Significant nonvalence quarks contribution in particular to baryon production. Gluon dominance at RHIC energies measured through breakdown of mt-scaling and baryon/meson ratio. Unexpected small effect on baryon/antibaryon ratio Is there a way to distinguish between fragmentation and recombination ? Does it matter ?
What will happen at the LHC ? What has happened in AA collisions (hadronization in matter) ?
0 in pp: well described by NLO p+p->0 + X
Thermallyshaped Soft Production
“Well Calibrated” Hard Scattering
Ingredients (via KKP or Kretzer) pQCD Parton distribution functions Fragmentation functions hep-ex/0305013 S.S. Adler et al.
Hadronization in QCD (the factorization theorem) Jet: A localized collection of hadrons which come from a fragmenting parton
hadrons
c
a
Parton Distribution Functions Hard-scattering cross-section
b
d hadrons
Fragmentation Function
leading particle
High pT (>~ 2.0 GeV/c) hadron production in pp collisions: h d pp
0 D d 2 2 h/c K dx dx f ( x , Q ) f ( x , Q ) ( ab cd ) a b a a b b 2 dyd pT dtˆ zc abcd
“Collinear factorization”
Modification of fragmentation functions (hep-ph/0005044)
RAA and high-pT suppression STAR, nucl-ex/0305015
pQCD + Shadowing + Cronin
energy loss
pQCD + Shadowing + Cronin + Energy Loss
Deduced initial gluon density at t0 = 0.2 fm/c dNglue/dy ≈ 800-1200 ≈ 15 GeV/fm3, eloss = 15*cold nuclear matter (compared to HERMES eA) (e.g. X.N. Wang nucl-th/0307036)
Is the fragmentation function modification universal ? Modification according to Gyulassy et al. (nucl-th/0302077)
Octet baryon fragmentation function from statistical approach based on measured inclusive cross sections of baryons in e+e- annihilation:
Induced Gluon Radiation ~collinear gluons in cone “Softened” fragmentation
nchin jet : increases zin jet : decreases
Quite generic (universal) but attributable to radiative rather than collisional energy loss
z
z
Jet quenching I: hadrons are suppressed, photons are not
Energy dependence of RAA 0 nucl-ex/0504001
RAA at 4 GeV: smooth evolution with √sNN Agrees with energy loss models
37
Radiative energy loss in QCD Baier, Schiff and Zakharov, AnnRevNuclPartSci 50, 37 (2000)
BDMPS approximation: multiple soft collisions in a medium of static color charges Transport coefficient:
qˆ medium d q q 2
Medium-induced gluon radiation spectrum: Total medium-induced energy loss: L
C
Emed dz d
2
d 2 2 d q
dI LPM dI BetheHeitler qˆ S NC ddz lcoherent ddz
dI LPM ~ S qˆC L ~ S qˆL2 ddz
t formation L c
E independent of parton energy (finite kinematics E~log(E)) E L2 due to interference effects (expanding medium E~L)
“Jet quenching” = parton energy loss High-energy parton loses energy by rescattering in dense, hot medium.
q q
Described in QCD as medium effect on parton fragmentation: Medium modifies perturbative fragmentation before final hadronization in vacuo. Roughly equivalent to an effective shift in z:
D p h ( z, Q ) D 2
(med) p h
z ( z , Q ) D p h , Q2 1 E / E 2
Important for controlled theoretical treatment in pQCD: Medium effect on fragmentation process must be in perturbative q2 domain.
Mechanisms High energy limit: energy loss by gluon radiation. Two limits: (a) Thin medium: virtuality q2 controlled by initial hard scattering (LQS, GLV)
L q
q g
q2
(b) Thick medium: virtuality controlled by rescattering in medium (BDMPS) Trigger on leading hadron (e.g. in RAA) favors case (a). Low to medium jet energies: Collisional energy loss is competitive! Especially when the parent parton is a heavy quark (c or b).
L q q
Extracting qhat from hadron suppression data
RAA: qhat~5-15 GeV2/fm
What does qhat qˆmeasure? 4 2 S N C qˆ mediumxGx, qˆL 2 NC 1
~RHIC data
QGP
Equilibrated gluon gas: number density ~T3 energy density ~T4 qˆ c
Hadronic matter
3 4
R. Baier, Nucl Phys A715, 209c
qhat+modelling energy density • pQCD result: c~2 (S? quark dof? …) • sQGP (multiplicities+hydro): c~10
Model uncertainties
q-hat at RHIC RHIC data
?
sQGP?
QGP
Pion gas Cold nuclear matter
BDMPS(ASW) vs. GLV Baier, Dokshitzer, Mueller, Peigne, Schiff, Armesto, Salgado, Wiedemann, Gyulassy, Levai, Vitev Salgado and Wiedemann PRD68 (2003) 014008
E ASWBDMPS
Medium-induced radiation spectrum
C qˆL2
2 qˆ 2 L
GLV
9 s3CR 4
Rough correspondence: (Wiedemann, HP2006)
2qˆ 0 0 d qˆ( ) L 0 L
EGLV
BDMPS
2
GeV fm GeV 2 qˆ 5 fm
qˆ 10
sCR 2 qˆ L 4
30-50 x cold matter density
1 dN g 2 Llog E / R dy
dN g 1800 dy dN g 900 dy
What do we learn from RAA? GLV formalism
BDMPS formalism ~15 GeV
Wicks et al, nucl-th/0512076v2 Renk, Eskola, hep-ph/0610059
E=15 GeV
Energy loss distributions very different for BDMPS and GLV formalisms But RAA similar! Need more differential probes
RAA for 0: medium density I I. Vitev
C. Loizides hep-ph/0608133v2
Use RAA to extract medium density:
W. Horowitz
I. Vitev: 1000 < dNg/dy < 2000 W. Horowitz: 600 < dNg/dy < 1600 C. Loizides: 6 < qˆ < 24 GeV2/fm
Statistical analysis to make optimal use of data Caveat: RAA folds geometry, energy loss and fragmentation
Different partons lose different amounts of energy 1.) heavy quark dead cone effect : 2.) gluon vs. quark energy loss: Heavy quarks in the vacuum and in Gluons should lose more energy the medium (Dokshitzer and and have higher particle Kharzeev (PLB 519 (2001) 199)) the multiplicities due to the color factor radiation at small angles is effect. suppressed Yu.Dokshitzer
…but everything looks the same at high pt…. up,down
strange
charm ?
Particle dependencies: RAA of strangeness A remarkable difference between RAA and RCP that seems unique to strange baryons. Ordering with strangeness content. ‘Canonical suppression’ is unique to strange hadrons
This effect must occur ‘between’ pp and peripheral AA collisions
Strange enhancement vs. charm suppression ?
Do strange particles hadronize different than charm particles ?
But is it a flavor effect ? Kaon behaves like D-meson, we need to measure Lc
An important detail: the medium is not totally opaque There are specific differences to the flavor of the probe plus: heavy quarks also show effects of collisional e-loss Experiment: there are baryon/meson differences
Theory: there are two types of e-loss: radiative and collisional, plus dead-cone effect for heavy quarks Flavor dependencies map out the process of in-medium modification
BUT: heavy quarks show same e-loss than light quarks
RAA of electrons from heavy flavor decay
Describing the suppression is difficult for models radiative energy loss with typical gluon densities is not enough (Djordjevic et al., PLB 632(2006)81) models involving a very opaque medium agree better (qhat very high !!) (Armesto et al., PLB 637(2006)362) collisional energy loss / resonant elastic scattering (Wicks et al., nucl-th/0512076, van Hees & Rapp, PRC 73(2006)034913) heavy quark fragmentation and dissociation in the medium → strong suppression for charm and bottom (Adil & Vitev, hep-ph/0611109)
Constraining medium viscosity /s Simultaneous description of STAR R(AA) and PHENIX v2 for charm. (Rapp & Van Hees, PRC 71, 2005) Ads/CFT == /s ~ 1/4 ~ 0.08 Perturbative calculation of D (2t) ~6 (Teaney & Moore, PRC 71, 2005) == /s~1 transport models require small heavy quark relaxation time small diffusion coefficient DHQ x (2T) ~ 4-6 this value constrains the ratio viscosity/entropy /s ~ (1.3 – 2) / 4 within a factor 2 of conjectured lower quantum bound consistent with light hadron v2 analysis electron RAA ~ 0 RAA at high pT - is bottom suppressed as well?
Energy density of matter
high energy density: > 1011 J/m3 P > 1 Mbar I > 3 X 1015W/cm2 Fields > 500 Tesla QGP energy density > 1 GeV/fm3 i.e. > 1030 J/cm3
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